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6–2C What is external forced convection? How does it differ from internal forced convection? Can a heat transfer system involve both internal and external convection at the same time? Give an example.
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6–3C In which mode of heat transfer is the convection heat transfer coefficient usually higher, natural convection or forced convection? Why
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6–4C Consider a hot baked potato. Will the potato cool faster or slower when we blow the warm air coming from our lungs on it instead of letting it cool naturally in the cooler air in the room? Explain
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6–5C What is the physical significance of the Nusselt number? How is it defined
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6–6C When is heat transfer through a fluid conduction and when is it convection? For what case is the rate of heat transfer higher? How does the convection heat transfer coefficient differ from the thermal conductivity of a fluid
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6–7C Define incompressible flow and incompressible fluid. Must the flow of a compressible fluid necessarily be treated as compressible
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6–8 During air cooling of potatoes, the heat transfer coefficient for combined convection, radiation, and evaporation is determined experimentally to be as shown:
Consider a 10-cm-diameter potato initially at 20˚C with a thermal conductivity of 0.49 W/m ˚C. Potatoes are cooled by refrigerated air at 5˚C at a velocity of 1 m/s. Determine the initial rate of heat transfer from a potato, and the initial value of the temperature gradient in the potato at the surface
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6–9 An average man has a body surface area of 1.8 m2 and a skin temperature of 33˚C. The convection heat transfer coefficient for a clothed person walking in still air is expressed as h = 8.6V0.53 for 0.5 < V < 2 m/s, where V is the walking velocity in m/s. Assuming the average surface temperature of the clothed person to be 30˚C, determine the rate of heat loss from an average man walking in still air at 10˚C by convection at a walking velocity of (a) 0.5 m/s, (b) 1.0 m/s, (c) 1.5 m/s, and (d) 2.0 m/s
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6–10 The convection heat transfer coefficient for a clothed person standing in moving air is expressed as h = 14.8V0.69 for 0.15 < V < 1.5 m/s, where V is the air velocity. For a person with a body surface area of 1.7 m2 and an average surface temperature of 29˚C, determine the rate of heat loss from the person in windy air at 10˚C by convection for air velocities of (a) 0.5 m/s, (b) 1.0 m/s, and (c) 1.5 m/s
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6–11 During air cooling of oranges, grapefruit, and tangelos, the heat transfer coefficient for combined convection, radiation, and evaporation for air velocities of 0.11 < V < 0.33 m/s is determined experimentally and is expressed as h = 5.05 kairRe1/3/D, where the diameter D is the characteristic length. Oranges are cooled by refrigerated air at 5˚C and 1 atm at a velocity of 0.5 m/s. Determine (a) the initial rate of heat transfer from a 7-cm-diameter orange initially at 15˚C with a thermal conductivity of 0.50 W/m ˚C, (b) the value of the initial temperature gradient inside the orange at the surface, and (c) the value of the Nusselt number.
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6–12C What is viscosity? What causes viscosity in liquids and in gases? Is dynamic viscosity typically higher for a liquid or for a gas
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6–13C What is Newtonian fluid? Is water a Newtonian fluid
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6–14C What is the no-slip condition? What causes it
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6–15C Consider two identical small glass balls dropped into two identical containers, one filled with water and the other with oil. Which ball will reach the bottom of the container first? Why
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6–16C How does the dynamic viscosity of (a) liquids and (b) gases vary with temperature
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6–17C What fluid property is responsible for the development of the velocity boundary layer? For what kind of fluids will there be no velocity boundary layer on a flat plate
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6–18C What is the physical significance of the Prandtl number? Does the value of the Prandtl number depend on the type of flow or the flow geometry? Does the Prandtl number of air change with pressure? Does it change with temperature
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6–19C Will a thermal boundary layer develop in flow over a surface even if both the fluid and the surface are at the same temperature? Laminar and Turbulent Flows
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6–20C How does turbulent flow differ from laminar flow? For which flow is the heat transfer coefficient higher
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6–21C What is the physical significance of the Reynolds number? How is it defined for external flow over a plate of length L
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6–22C What does the friction coefficient represent in flow over a flat plate? How is it related to the drag force acting on the plate?
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6–23C What is the physical mechanism that causes the friction factor to be higher in turbulent flow
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6–24C What is turbulent viscosity? What is it caused by
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6–25C What is turbulent thermal conductivity? What is it caused by?
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6–26C Under what conditions can a curved surface be treated as a flat plate in fluid flow and convection analysis
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6–27C Express continuity equation for steady twodimensional flow with constant properties, and explain what each term represents
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6–28C Is the acceleration of a fluid particle necessarily zero in steady flow? Explain
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6–29C For steady two-dimensional flow, what are the boundary layer approximations
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6–30C For what types of fluids and flows is the viscous dissipation term in the energy equation likely to be significant
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6–31C For steady two-dimensional flow over an isothermal flat plate in the x-direction, express the boundary conditions for the velocity components u and v, and the temperature T at the plate surface and at the edge of the boundary layer
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6–32C What is a similarity variable, and what is it used for? For what kinds of functions can we expect a similarity solution for a set of partial differential equations to exist
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6–33C Consider steady, laminar, two-dimensional flow over an isothermal plate. Does the thickness of the velocity boundary layer increase or decrease with (a) distance from the leading edge, (b) free-stream velocity, and (c) kinematic viscosity
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6–34C Consider steady, laminar, two-dimensional flow over an isothermal plate. Does the wall shear stress increase, decrease, or remain constant with distance from the leading edge
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6–35C What are the advantages of nondimensionalizing the convection equations
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6–36C Consider steady, laminar, two-dimensional, incompressible flow with constant properties and a Prandtl number of unity. For a given geometry, is it correct to say that both the average friction and heat transfer coefficients depend on the Reynolds number only
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6–37 Oil flow in a journal bearing can be treated as parallel flow between two large isothermal plates with one plate moving at a constant velocity of 12 m/s and the other stationary. Consider such a flow with a uniform spacing of 0.7 mm between the plates. The temperatures of the upper and lower plates are 40˚C and 15˚C, respectively. By simplifying and solving the continuity, momentum, and energy equations, determine (a) the velocity and temperature distributions in the oil, (b) the maximum temperature and where it occurs, and (c) the heat flux from the oil to each plate.
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6–38 Repeat Problem 6–37 for a spacing of 0.4 mm
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6–39 A 6-cm-diameter shaft rotates at 3000 rpm in a 20-cmlong bearing with a uniform clearance of 0.2 mm. At steady operating conditions, both the bearing and the shaft in the vicinity of the oil gap are at 50˚C, and the viscosity and thermal conductivity of lubricating oil are 0.05 N s/m2 and 0.17 W/m K. By simplifying and solving the continuity, momentum, and energy equations, determine (a) the maximum temperature of oil, (b) the rates of heat transfer to the bearing and the shaft, and (c)the mechanical power wasted by the viscous dissipation in the oil.
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6–40 Repeat Problem 6–39 by assuming the shaft to have reached peak temperature and thus heat transfer to the shaft to be negligible, and the bearing surface still to be maintained at 50˚C
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6–41 Reconsider Problem 6–39. Using EES (or other) software, investigate the effect of shaft velocity on the mechanical power wasted by viscous dissipation. Let the shaft rotation vary from 0 rpm to 5000 rpm. Plot the power wasted versus the shaft rpm, and discuss the results
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6–42 Consider a 5-cm-diameter shaft rotating at 2500 rpm in a 10-cm-long bearing with a clearance of 0.5 mm. Determine the power required to rotate the shaft if the fluid in the gap is (a) air, (b) water, and (c) oil at 40˚C and 1 atm
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6–43 Consider the flow of fluid between two large parallel isothermal plates separated by a distance L. The upper plate is moving at a constant velocity of and maintained at temperature T0 while the lower plate is stationary and insulated. By simplifying and solving the continuity, momentum, and energy equations, obtain relations for the maximum temperature of fluid, the location where it occurs, and heat flux at the upper plate
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6–44 Reconsider Problem 6–43. Using the results of this problem, obtain a relation for the volumetric heat generation rate g ·, in W/m3. Then express the convection problem as an equivalent conduction problem in the oil layer. Verify your model by solving the conduction problem and obtaining a relation for the maximum temperature, which should be identical to the one obtained in the convection analysis
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6–45 A 5-cm-diameter shaft rotates at 4500 rpm in a 15-cmlong, 8-cm-outer-diameter cast iron bearing (k = 70 W/m K) with a uniform clearance of 0.6 mm filled with lubricating oil (u=0.03 N . s/m2 and k = 0.14 W/m K). The bearing is cooled externally by a liquid, and its outer surface is maintained at 40˚C. Disregarding heat conduction through the shaft and assuming one-dimensional heat transfer, determine (a) the rate of heat transfer to the coolant, (b) the surface temperature of the shaft, and (c) the mechanical power wasted by the viscous dissipation in oil.
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6–46 Repeat Problem 6–45 for a clearance of 1 mm.
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6–47C How is Reynolds analogy expressed? What is the value of it? What are its limitations
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6–48C How is the modified Reynolds analogy expressed? What is the value of it? What are its limitations
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6–49 A 4-m x 4-m flat plate maintained at a constant temperature of 80˚C is subjected to parallel flow of air at 1 atm, 20˚C, and 10 m/s. The total drag force acting on the upper surface of the plate is measured to be 2.4 N. Using momentum-heat transfer analogy, determine the average convection heat transfer coefficient, and the rate of heat transfer between the upper surface of the plate and the air.
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6–50 Ametallic airfoil of elliptical cross section has a mass of 50 kg, surface area of 12 m2, and a specific heat of 0.50 kJ/kg ˚C). The airfoil is subjected to air flow at 1 atm, 25˚C, and 8 m/s along its 3-m-long side. The average temperature of the airfoil is observed to drop from 160˚C to 150˚C within 2 min of cooling. Assuming the surface temperature of the airfoil to be equal to its average temperature and using momentum-heat transfer analogy, determine the average friction coefficient of the airfoil surface.
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6–51 Repeat Problem 6–50 for an air-flow velocity of 12 m/s
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6–52 The electrically heated 0.6-m-high and 1.8-m-long windshield of a car is subjected to parallel winds at 1 atm, 0˚C, and 80 km/h. The electric power consumption is observed to be 50 W when the exposed surface temperature of the windshield is 4˚C. Disregarding radiation and heat transfer from the inner surface and using the momentum-heat transfer analogy, determine drag force the wind exerts on the windshield
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6–53 Consider an airplane cruising at an altitude of 10 km where standard atmospheric conditions are -50˚C and 26.5 kPa at a speed of 800 km/h. Each wing of the airplane can be modeled as a 25-m x 3-m flat plate, and the friction coefficient of the wings is 0.0016. Using the momentum-heat transfer analogy, determine the heat transfer coefficient for the wings at cruising conditions.
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